Question

The article The Influence of Temperature and Sunshine on the Alpha-Acid Contents of Hops t reports the following data on yield (y), mean temperature over the period between date of coming into hops and date of picking (x1), and mean percentage of sunshine during the same period (x2) for the Fuggle variety of hop 16.7 17.418.4 16.8 18.9 17.1 17.3 18.2 21.3 21.2 20.7 18.5 30 42 47 47 43 48 43 50 56 60 41 210 110 103 103 91 76 73 70 68 53 45 31 Use the following R Code to complete the regression analysis x1-c16.7,17.4,18.4,16.8,18.9,17.1,17.3,18.2,21.3,21.2,20.7,18.5) x2-c(30,42,47,47,43,41,48,44,43,50,56,60) y-c(210,110,103,103,91,76,73,70,68,53,45,31) mod Im(y x1+x2) summary(mod) (a)According to the output, what is the least squares regression equation y . botb +b2x2 : (Round each value to 3 decimal places.) X1+ (b) what is the estimate for ơ? (Hint: This is referred to as the residual standard error in R output) (c) According to the model what is the predicted value for y when x1-21.3 and X2 = 43 and what is the corresponding residual? (Round your answers to four decimal places.) Residual: y-y- (d) Test Ho: β1-82 . 0 versus Ha: either β1 or β2 +0 From the output state the test statistic and the p-value. Round your test stat to one decimal place and your p-value to 4 decimal places.) p-value State the conclusion in the problem context. O There is moderately suggestive evidence at least one of the explanatory variables is a significant predictor of the response O There is no suggestive evidence at least one of the explanatory variables is a significant predictor of the response O There is convincing evidence at least one of the explanatory variables is a significant predictor of the response There is slightly suggestive evidence at least one of the explanatory vanables is a significant predictor of the response (e) The estimated standard deviation of y when x1 = 2 1.3 and X2 = 43 is s-16.58. Use this to obtain the 95% CI forly. 21.3, 43. (Round your answers to two decimal places.) (f) Use the information in parts (b) and (e) to obtain a 95% PI for yield in a future experiment when x1 21.3 and X2 = 43, (Round your answers to two decimal places.) (g) Given that x2 is in the model, would you retain x1? O Yes, there is evidence this factor is significant. It should remain in the model O No, there isn't evidence this factor is significant. It should be dropped from the model

Answer 1

Answer:

a)

MINITAB output: Regresslon Analysis: Y versus X1, X2 Analysis of Variance DF Adj SS Adj MS F-Value P-Value Regression 17817 8908.4 14.90 0.001 0.208 Source 1.84 x1 1 1101 1100.8 X2 1 10571 10571.2 17.68 0.002 5382 598.0 Error Total 11 23199 Model Summary S R-sq R-sq (adj) R-sq(pred) 24.4545 76.80 71 , 64 48.68% Coefficients Term Coef SE Coef T-Value P-Valu VIF Constant 415.1 82.5 5.03 0.001 -6.59 4.86 0.208 1.22 x1 -1 X2 -4.50 1.07 -4.20 0.002 1.22 Regression Equation Y = 415.1-6.59 X1-4.50 X2 Fits and Diagnostics for Unusual Observations Std obs Fit Resid Resid 1 210.0 169.9 40.1 2.29 R R Large residual

From MINITAB output, the regression equation is, y = 415.1-659a-450x,

Find the residual standard eror. From MINITAB output, the value ofs 24.4545

c)

MINITAB output: Prediction for Y Regression Equation 415.1-6.59 X1-4.50 X2 Y Variable Setting X1 21.3 43 X2 Eit SEFİt 95% CI 95% PI 81.0336 16.5815 (43.5238, 118.543) (14.1959, 147.871) From MINITAB output, the predicted value is 81.0336

From MINITAB output, the value of Fis 184 and p-value is 0.208. The conclusion is There is significantly suggest evidence at least one of the explanatory variables is a significance predictor of the response.

From MINITAB output, the 95% confidence interval is k 43.52, 1 18, 541

From MINITAB output, the 95% prediction interval is (14.19, 14.87)

Yes, there is evidence this factor is significant. It should remain in themodel.